Bayesian Estimation of ARCH-Type Volatility Models

Empirical evidence abounds that asset returns exhibit characteristics such as volatility clustering, asymmetry, and heavy‐tailedness. Volatility clustering describes the tendency of returns to alternate between periods of high volatility and low volatility. In addition, volatility responds asymmetrically to positive and negative return shocks—it tends to be higher when the market falls than when it rises. The nonconstancy of volatility has been suggested as an underlying reason for returns’ fat tails. Volatility models attempt to systematically explain these stylized facts about asset returns. The Bayesian methodology offers distinct advantages over the classical framework in estimating volatility models. Parameter restrictions, such as stationarity restriction, are notoriously difficult to handle within the frequentist setting and straightforward to implement in the Bayesian one. The MCMC numerical simulation methods facilitate greatly the estimation of complex volatility models, such as Markov‐switching volatility models.